EXCHANGE 


A  Study  of  the  Initial  Velocity  in  the  Hydrolysis 
of  Sucrose  by  Invertase. 


DISSERTATION 

Submitted  in  Partial  Fulfillment  of  the  requirements 

for  the  Degree  of  Doctor  of  Philosophy  in 

the  Faculty  of  Pure  Science  of 

Columbia  University. 


BY 

HAROLD  LESTER  SIMONS,  A.B.,  A.M. 

NEW  YORK   CITY 
1921 


A  Study  of  the  Initial  Velocity  in  the  Hydrolysis 
of  Sucrose  by  Invertase. 


DISSERTATION 

Submitted  in  Partial  Fulfillment  of  the  requirements 

for  the  Degree  of  Doctor  of  Philosophy  in 

the  Faculty  of  Pure  Science  of 

Columbia  University. 


BY 

HAROLD  LESTER  SIMONS,  A.B.,  A.M. 

NEW  YORK   CITY 
1921 


TO   MY 
FATHER  AND   MOTHER 


^51732 


ACKNOWLEDGMENT 

The  author  desires  to  express  his  gratitude  to 
Professor  J.  M.  Nelson,  at  whose  suggestion  this  work 
was  carried  out.  To  his  fruitful  suggestions  and  to 
his  kindly  encouragement,  this  research  owes  what- 
ever merit  it  may  possess. 


ABSTRACT  OF  DISSERTATION 

1.  What  was  attempted  ? 

2.  In  how  far  were  the  attempts  successful? 

3.  What  contribution  actually  new  to  the  science  of  Chem- 

istry has  been  made  ? 

1.  In  view  of  the  fact  that  many  investigators  have  ex- 
trapolated the  initial  portion  of  the  curve  representing  the 
hydrolysis  of  sucrose  by  invertase  by  assuming  that  the  func- 
tion was  initially  linear  and  due  to  the  importance  of  knowing 
the  actual  course  of  the  inversion  at  its  start,  an  attempt  has 
been  made  to  determine : 

(a)  Whether  this  condition  actually  exists ; 

(b)  In  the  case  of  its  actual  existence,  whether  it  is  due 
to  lack  of  sufficiently  great  experimental  precision  or  is  due  to 
some  peculiarity  in  the  reaction. 

2.  It  has  been  found  that 

(a)  In  general,  the  initial  course  of  the  curve  represent- 
ing the  hydrolysis  is  linear ; 

(b)  Under  certain  conditions,  however,  the  velocity  ac- 
tually rises  to  a  maximum  ; 

(c)  The  observed  linear  part  of  the  curve  is  due  mainly 
to  a  peculiarity  of  the  reaction. 

3.  It  has  been  shown  that 

(a)  By  actual  measurement  the  velocity  of  the  inversion 
of  sucrose  by  invertase  is,  in  general,  constant  at  the  start.  Thsi 
is  the  usual  case  even  in  the  presence  of  added  substances. 
However,  under  certain  conditions,  the  velocity  has  been  ob- 
served to  go  through  a  maximum  before  the  gradual  decrease 
sets  in ; 

(b)  This  constant  or  increasing  velocity  is  only  evident  at 
the  beginning  of  the  hydrolysis  ; 

7 


(c)  These  observations — particularly  in  view  of  the  fact 
that  the  initial  velocity  at  times  increases — strongly  indicate 
that  invertase  action  involves  a  series  of  consecutive  reactions ; 

(d)  Since  the  velocity  often  increases  to  a  maximum  dur- 
ing the  earlier  part  of  the  reaction,  the  initial  velocity  cannot 
be  taken  as  a  true  measure  of  the  activity  of  the  invertase.    In 
the  light  of  this  fact,  the  theory  of  invertase  action  proposed 
by  Colin  and  Chaudun  (which  depends  upon  the  assumption 
that  the  rate  of  combination  between  sucrose  and  invertase  is 
infinite)  is  untenable.     This  criticism  likewise  applies  to  the 
theory  advanced  by  Michaelis  and  Menten  which  fails  to  ac- 
count for  some  other  facts  disclosed  by  this  investigation. 


A  STUDY  OF  THE  INITIAL  VELOCITY  IN  THE 
HYDROLYSIS  OF  SUCROSE  BY  INVERTASE 


In  determining  the  activity  of  hydrolytic  enzymes,  like 
invertase,  the  question  arises  as  to  what  extent  the  velocity  of 
the  hydrolysis  of  the  substrate  can  be  taken  as  a  measure  of 
the  activity  or,  in  other  words,  how  much  of  the  enzyme  pres- 
ent in  the  solution  is  in  the  active  condition. 

Henri1  proposed 

Kt=  (1  +na)ln-       -+  (m  — n)x (1) 

a — x 

as  an  equation  for  representing  the  kinetics  for  the  hydrolysis 
of  cane  sugar  by  invertase.  In  his  derivation  of  this  equation 
(1),  he  like  many  others  (Brown2)  assumed  one  unit  of  inver- 
tase to  combine  (reversibly  according  to  the  Mass  Law)  with 
one  mole  of  cane  sugar  and  also  with  the  inverted  cane  sugar 
as  it  was  formed  in  the  reaction.  The  terms  m  and  n  in  the 
equation  are  the  equilibrium  constants  of  the  cane  sugar — in- 
vertase and  inverted  cane  sugar — invertase  compounds  re- 
spectively. The  K  is  the  velocity  coefficient  of  the  hydrolysis, 
and  a — x  and  x  represent  the  concentrations  of  the  cane  sugar 
and  inverted  cane  sugar  at  the  time  t.  He  also  assumed  that 
the  velocity  of  combination  between  the  enzyme  and  sugars 
is  infinite  when  compared  to  the  velocity  of  hydrolysis. 
Henri  was  unable  to  obtain  experimental  values  for  the  mass 
law  constants  (m  and  n)  and  therefore  resorted  to  a  method 
based  upon  trial,  assigning  to  m  and  n  arbitrary  values  which 
gave  fairly  constant  values  for  the  velocity  coefficient,  K. 

Hudson3  objected  to  Henri's  results  on  the  ground  that 
the  latter  had  followed  the  course  of  the  hydrolysis  by  permit- 
ting the  reaction  to  take  place  in  a  polariscope  tube  and  notic- 
ing the  change  in  rotation  of  the  sugar  solution  from  time  to 
time.  The  rotation  values  obtained  in  this  way  involve  an 
error,  since  the  <x  glucose  and  <*  fructose  which  are  liberated 
from  the  cane  sugar  and  undergo  muta-rotation  into  their  re- 
spective equilibrium  mixtures  of  oc  and  ft  isomers  but  slowly 

9 


under  the  acidity  conditions  which  prevail  in  invertase  reac- 
tions. When  this  error  is  avoided,  then  Hudson  claims  from 
his  own  results  that  the  velocity  of  hydrolysis  becomes  directly 
proportional  to  the  concentration  of  the  cane  sugar  present, 
or  in  other  words,  that  the  reaction  is  mono-molecular  and 
similar  to  acid  hydrolysis.  In  spite  of  Hudson's  results,  which 
might  belong  to  some  special  case,  it  has  been  quite  firmly  es- 
tablished that  invert  sugar,  glucose  and  fructose  exert  a  re- 
tarding influence  on  the  velocity  when  cane  sugar  is  hydrolyzed 
by  invertase.  (vide  —  Brown2,  Armstrong4,  and  others.) 

Michaelis  and  Menten's  Method  for  Determining  the 
Dissociation  Constant  of  Sugar-invertase  Compounds. 

Michaelis  and  Menten5,  adopting  Henri's  theory  concern- 
ing the  mechanism  of  invertase  action,  proposed  a  method  for 
determining  experimentally  the  dissociation  constants  of  the 
invertase-cane  sugar  and  invertase-invert  sugar  compounds 
(i.  e.  —  m  and  n  in  equation  (1)  )  and  thereby  avoiding  the  diffi- 
culty encountered  by  Henri,  whose  equation  contained  three 
unknowns.  According  to  them,  at  the  beginning  of  the  hy- 
drolysis only  cane  sugar,  cane  sugar-invertase  compound  and 
water  are  present  in  the  solution  ;  and  the  velocity  of  hydrolysis 
is  then  assumed  to  be  proportional  to  the  concentration  of  the 
cane  sugar-invertase  compound.  Since  in  this  theory  the  Mass 
Law  is  considered  to  hold,  by  varying  the  initial  concentra- 
tion of  the  cane  sugar  and  comparing  the  velocities  correspond- 
ing to  these  different  concentrations,  they  derive  a  relationship  : 

S 
V  =  -  ..................  (2) 

S  +  m 
which  is  similar  in  form  to 

H+ 


H+  +  k 

Equation  (3)  is  the  expression  for  the  ionization  of  an 
acid  in  which  the  symbols  have  their  customary  significance. 


NOTE — By  plotting  the  concentration  of  the  undissociated  acid 
(1 — oc  )  as  ordinates  and  the  logarithms  of  the  concentration  of  the 
hydrogen  ion,  H+,  as  abscissas,  a  curve  is  obtained  from  which  the 
value  of  the  dissociation  constant  can  be  obtained  graphically. 

10 


In  equation  (2)  S  is  the  concentration  of  the  free  cane 
sugar  and  corresponds  to  H+  in  (3),  V  is  proportional  to  the 
velocity  of  hydrolysis  of  the  cane  sugar  and  therefore  is  di- 
rectly proportional  to  the  concentration  of  the  undissociated 
cane  sugar-invertase  compound  and  hence  corresponds  to 
(1  —  GC  )  in  (3).  Therefore  the  dissociation  constant,  m,  of 
the  cane  sugar-invertase  combination  can  be  obtained  graphi- 
cally just  as  the  ionization  constant,  K,  in  equation  (3)  can  be 
determined.  As  a  consequence  of  this  idea,  n  is  resolved  into 
two  constant  —  one  for  glucose  and  the  other  for  fructose,  in 
combination  with  invertase.  Each  of  these  constants  is  deter- 
mined by  hydrolyzing  the  cane  sugar  in  the  presence  of  definite 
amounts  of  glucose  or  fructose,  since  the  monose  is  considered 
to  combine  with  a  certain  amount  of  the  enzyme  and  thereby 
leaves  less  invertase  to  combine  with  and  hydrolyze  the  cane 
sugar.  If  I  represents  the  total  enzyme  present,  P  the  amount 
combined  with  the  cane  sugar  and  T  the  amount  combined 
with  the  glucose  (or  fructose,  as  the  case  may  be),  then  the  dis- 
sociation constant  of  the  cane  sugar  invertase  compound  can 
be  represented  by 

Sx  (I—  P  —  T) 
m  =  --  ................  (4) 

P 
and  that  for  the  glucose-invertase  compound  by 

G+  (I  —  P  —  T)' 
n  =  --  ................  (5) 

T 

in  which  equation  S  and  G  are  the  concentrations  of  free  cane 
sugar  and  free  glucose  respectively.     Since  the  velocity  of  hy- 
drolysis is  considered  proportional  to  the  concentration  of  the 
cane  sugar-invertase  compound,  the  relation  between  the  ini- 
tial velocities  when  glucose  is  present  and  when  it  is  absent 
can  be  expressed  by  the  equation 

V:V0  =  P:P0  .......................  (6) 

in  which  P  and  P0  are  the  concentrations  of  the  invertase-cane 
sugar  compound  when  glucose  is  present  and  when  it  is  ab- 
sent.    By  combining  (4),  (5)  and  (6)  the  expression 
Cm 


n= 


11 


is  obtained,  in  which  all  the  terms  except  n  are  known  or  cap- 
able of  measurement.  It  was  stated  above  that  in  measuring 
the  relative  velocities  of  hydrolysis  of  the  cane  sugar  both  in 
the  absence  and  presence  of  invert  sugar,  glucose  or  fructose, 
Michaelis  and  Menten  made  use  of  the  initial  velocities  in  each 
case.  They  considered  the  velocity  to  be  sufficiently  constant 
at  the  beginning  of  the  reaction  so  that  the  initial  portion  A  in 
Figure  III  of  the  hydrolysis  curve,  obtained  by  plotting  the 
change  in  rotation  of  the  solution  as  ordinates  and  time  as 
abscisas,  would  be  practically  a  straight  line  and  its  slope  with 
the  time  axis  would  be  therefore  the  amount  of  cane  sugar 
hydrolyzed  divided  by  the  time,  or  a  measure  of  the  velocity. 

In  Figure  III  is  given  the  general  shape  of  a  curve  for  the 
hydrolysis  of  cane  sugar  when  either  invertase  or  acid  is  used 
as  the  catalyst.  Acid  hydrolysis  of  cane  sugar  obeys  quite  well 
the  mono-molecular  law, 

1               a 
k  =  — log-          - (8), 

t  a  —  x 

in  which  k  is  the  velocity  coefficient  and  a  is  the  initial  Concen- 
tration of  the  cane  sugar.  When  x,  the  amount  of  cane  sugar 
hydrolyzed  is  plotted  against  the  corresponding  time,  t,  it  will 
be  found  that  the  initial  portion  A  of  the  curve  is  such  in  shape 
that  it  cannot  be  distinguished  from  a  straight  line  by  inspec- 
tion, although  from  (8)  it  is  known  to  be  logarithmic.  The 
general  shape  of  the  curve  obtained  when  cane  sugar  is  hydro- 
lyzed by  invertase  is  similar  to  that  obtained  when  acid  is  used, 
the  only  difference  being  that  in  most  cases  when  the  velocity 
coefficients  are  calculated  according  to  the  mono-molecular 
law  with  invertase  as  the  catalyst,  it  is  found  that  they  in- 
crease during  the  major  portion  of  the  reaction.  This  means 
that  the  invertase  curve,  in  general,  bends  less  towards  the 
time  axis  than  the  acid  curve. 

Let  us  grant  that  is  permissible  to  consider  the  portion  of 
the  hydrolysis  curve  corresponding  to  A  in  Figure  III  as  the 
tangent  to  the  curve  at  the  beginning  of  the  reaction  and  that 
it  can  be  used  as  a  measure  of  the  initial  velocity  without  in- 
troducing very  much  of  an  error.  But  Michaelis  and  Menten 
followed  the  same  procedure  when  measuring  retardation  due 

12 


to  invert  sugar,  glucose  or  fructose.  Adding  invert  sugar,  glu- 
cose or  fructose — the  orders  of  the  magnitude  of  the  retarda- 
tion of  glucose  and  fructose  upon  the  reaction  are  the  same — 
t®  the  cane  sugar  solution  before  the  hydrolysis  by  the  enzyme 
has  commenced  is  equivalent  to  moving  the  origin  of  the  hy- 
drolysis curve  up  into  the  B  portion  of  the  curve  in  Figure  III 
because  the  composition  of  the  sugar  solution  under  these  con- 
ditions would  be  the  same  as  that  of  a  cane  sugar  solution 
which  had  been  undergoing  hydrolysis  for  some  time.  If  the 
products  of  the  hydrolysis  of  the  cane  sugar  by  invertase  have 
the  same  influence  upon  the  reaction  when  added  before  the 
beginning  of  the  reaction,  it  is  evident  that  the  first  few  experi- 
mentally determined  points  on  the  curve  cannot  lie  on  a  straight 
line,  because  the  curvature  is  so  much  more  pronounced  in  the 
B  portion  than  in  the  A.  In  other  words,  it  is  not  possible 
(due  to  the  shape  of  the  B  portion)  for  a  curve  drawn  through 
the  first  few  experimentally  determined  points  to  be  sufficiently 
linear  so  that  it  can  be  regarded  as  tangent  to  the  hydrolysis 
curve  at  the  beginning  when  the  origin  of  the  curve  lies  in  B — 
as  is  the  case  when  glucose  or  invert  sugar  have  been  added 
previous  to  the  start  of  the  reaction.  On  the  other  hand,  if 
the  first  few  points  do  fall  on  a  straight  line  or  approximately 
straight  line,  as  Michaelis  and  Menten  claim,  then  it  is  neces- 
sary to  conclude  that  the  influence  of  the  products  of  hydrolysis 
formed  during  the  course  of  the  hydrolysis  is  different  from 
the  influence  they  exert  when  added  before  the  beginning  of 
the  reaction. 

It  \vas  decided,  therefore,  to  examine  the  initial  velocity  of 
the  hydrolysis  of  cane  sugar  by  invertase  in  the  presence  and 
absence  of  glucose  and  invert  sugar  at  the  beginning  of  the 
reaction.  In  Table  I  are  recorded  the  results  obtained.  Sam- 
ples were  removed  from  the  solution  undergoing  hydrolysis 
every  five  minutes  during  the  first  25  minutes  of  the  reaction. 
The  enzyme  action  was  interrupted  in  the  removed  samples  by 
means  of  sodium  carbonate,  and  the  solutions  examined  in  a 
400  mm.  tube  in  a  polariscope.  (For  further  details  concern- 
ing the  experimental  procedure  see  the  experimental  part). 

13 


TABLE   I. 

Part  A.    1  cc.  Invertase  solution  per  100  cc.  of  solution.  Temperature  25° 
Hydrogen  ion  cone.  10"1-4  moles  per  liter. 


Cone,  of 


Rotation  after  the  reaction  had  continued  for-minutes 


Sucrose 

0 

5 

10 

15 

20 

25 

GO 

1.0% 

2.62° 

2.520 

2.420 

2.31° 

2.195° 

2.090 

-0.730 

1.5% 

3.91 

3.78 

3.65 

3.52 

3.40 

3.28 

—1.08 

2.0% 

5.21 

5.06 

4.92 

4.78 

4.65 

4.51 

—1.45 

3.0% 

7.80 

7.63 

7.48 

7.33 

7.18 

7.03 

—2.24 

4.0% 

10.39 

10.22 

10.08 

9.91 

9.75 

9.58 

—2.96 

5,0% 

13.00 

12.82 

12.655 

12.475 

12.32 

12.16 

—3.71 

6.0%, 

15.60 

15.45 

15.29 

15.13 

14.96 

14.82 

—4.51 

Part  B.    Same  solution  as  in  A  except  2  cc.  of  invertase 
solution  per  100  cc. 


Cone,  of 


Rotation  after  the  reaction  had  continued  for-minutes 


Sucrose 

0 

5 

10 

15 

20 

25 

CO 

1.0% 

2.666° 

2.445° 

2.235° 

2.033° 

1.843° 

1.6580 

—0.6550 

20% 

5.258 

4.980 

4.705 

4.433 

4.175 

3.924 

—1.42 

3.0% 

7.858 

7.539 

7.240 

6.936 

6.645 

6.357 

—2.17 

4.0% 

10.450 

10.124 

9.807 

9.479 

9.172 

8.867 

—2.92 

5.0% 

13.078 

12.748 

12.439 

12.116 

11.799 

11.500 

—3.65 

6.0% 

15.641 

15.303 

14.995 

14.673 

14.371 

14.073 

—4.41 

Part  C.    All  solutions  contain  1%  cone,  sugar  at  the  start,  but  varying 

cone,  of  added  glucose.     Cone,  of  invertase,  temperature 

and  hydrogen  ion  cone,  same  as  in  B. 


Cone,  of 


Rotation  after  the  reaction  had  continued  for-minutes 


Glucose 

0 

5 

10 

15 

20 

25 

GO 

0.0% 

2.666° 

2.445° 

2.235° 

2.033° 

1.843° 

1.658° 

—0.6550 

1.0% 

4.693 

4.519 

4.346 

4.171 

4.012 

3.855 

1.381 

3.0% 

8.793 

8.673 

8.537 

8.396 

8.262 

8.140 

5.475 

4.0% 

10.863 

10.765 

10.635 

10.503 

10.392 

10.285 

7.55 

NOTE — The  figures  above  are  the  averages  of  several  readings  for 
each  experiment  and  of  two  series  of  experiments.  An  estimation  of 
the  error  would  put  it  at  slightly  less  than  0.01°.  The  last  figures  in 
B  and  C  were  retained  as  an  average  rather  than  because  of  its  signifi- 
cance. Due  to  the  addition  of  sodium  carbonate  solution  and  the  pres- 
ence of  the  optically  active  invertase,  the  above  readings  do  not  corre- 
spond exactly  to  the  rotations  which  sugar  solutions  of  these  concen- 
trations would  have. 

14 


0  =A   }  Subtract  0.6° 
•  =  B   J  from  A&B 


5  10  15          20          25 

Minutes 

FIG.  I 

The  data  in  Table  I  show  that  all  these  sugar  solutions  have 
practically  constant  initial  velocities.  The  last  two  (Part  C) 
containing  3%  and  4%  glucose  appear  to  show  a  slight  in- 
crease in  velocity  during*  the  earlier  periods  of  the  reaction. 
This  effect  becomes  more  evident  when  the  results  are  plotted 
as  in  Figure  I.  In  the  light  of  the  above  results,  it  therefore 
appears  reasonable  to  regard  the  line  passing  through  the  first 

15 


few  experimentally  determined  points  on  the  hydrolysis  curve 
as  the  tangent  to  the  curve  at  its  origin.  In  other  words,  Mich- 
aelis  and  Menten's  method  of  determining  the  initial  velocity 
seems  to  be  all  right.  On  the  other  hand,  the  fact  that  the 
initial  velocity,  when  glucose  is  present  in  the  cane  sugar  solu- 
tion, is  constant  or  increasing  shows  that  a  difference  exists  be- 
tween it  and  the  velocity  after  the  initial  period  has  been  passed, 
as  was  suggested  in  the  discussion  of  the  difference  between  the 
A  and  B  portions  of  the  curve  in  Figure  III.  Consequently, 
there  appears  to  be  a  time  element  involved,  and  the  initial  ve- 
locity is  not  comparable  with  the  velocity  prevailing  after  the 
hydrolysis  has  been  going  on  for  some  time,  even  though  in  the 
two  cases  the  compositions  of  the  solutions  may  be  the  same. 
If  this  be  true  then  the  method  of  Michaelis  and  Menten,  which 
depends  upon  the  initial  velocities,  will  not  be  applicable  for 
measuring  the  actual  velocities  throughout  the  entire  course  of 
the  reaction. 

The  Initial  Velocity  Involves  a  'Time  Element. 

In  order  to  gain  more  evidence  concerning  this  time  element 
'which  appears  to  exist  between  a  reaction  beginning  and  one 
that  has  been  in  progress  for  some  time  the  following  experi- 
ments were  undertaken. 

Solution  A  contained  cane  sugar  and  invert  sugar  (equal 
amounts  of  glucose  and  fructose)  in  such  concentrations  as  to 
correspond  to  a  3%  cane  sugar  solution'  that  had  undergone 
hydrolysis  to  the  extent  of  about  42%.  The  initial  velocity  of 
hydrolysis  of  solution  A  was  found  to  be  constant  just  as  had 
been  observed  in  the  experiments  described  in  Table  I,  Part  C, 
and  the  values  are  given  in  Table  II,  Part  A. 

TABLE   II. 

Hydrogen  ion  cone.  =  10~4-4. 
Temp.=25°,  2.49  cc.  invertase  per  100  cc.  of  solution. 


1.740    gm.  Cane  Sugar 
0.6632    "     Glucose 
0.6632    "     Fructose 


B 


per  100          30    grms.    Cane    sugar    per 
cc.  Sol.          100  cc.  hydrolyzed  to  about 

42%. 

16 


Time 

0.0  (61.50) 

3.01  (64.51) 
6.00  (67.50) 

9.02  (70.52) 
12.01  (73.51) 
15.01  (76.51) 
18.01  (79.57) 


Rotation 
4.029° 
.3.847 
3.666 
3.487 
3.310 
3.148 
2.978 


Time        Rotation 

59.99  4.120° 

63.03  3.937 

66.00  3.776 

69.01  3.639 
72.01  3.502 
75.00  3.380 
78.03  3.283 


NOTE — These  results  are  the  mean  of  two  series  of  experiments. 
The  above  values  differ  by  no  more  than  0.005°  from  either  of  the  indi- 
vidual experimental  values. 

For  the  sake  of  comparison,  a  3%  cane  sugar  solution  B  was 

permitted  to  undergo  hydrolysisj  until  it  had  reached  about 
42%  inversion  of  the  cane  sugar.  At  this  point  the  composi- 
tion of  B  corresponded  to  approximately  that  of  the  initial  con- 
centration of  A.  The  velocity  of  hydrolysis  of  solution  B  was 
determined  after  it  had  passed  the  42%  hydrolyzed  stage  and 
compared  with  the  velocity  of  solution  A.  The  values  obtain- 
ed are  given  under  B  in  Table  II. 


flotation  in  Degrees  for  Table  I 

Minutes  for  TaP/eE 
1          2S         29         33          37          Ju         * 

2.20 
240 
2.60 
2BO 

/ 

/ 

^ 

" 

/A 

2 

/ 

V 

/ 

y 

o  = 

A  = 

B  ]  Table 

JL 

z 

9      ** 

D   - 

^Table 

m 

'60       64         68         72          76         80         84 

Minutes  for  Table! 

nan 

The  difference  between  the  velocities  of  solutions  A  and  B 
is  brought  out  more  clearly  by  means  of  the  curves  in  Figure 

17 


II.  In  order  that  these  curves  may  be  strictly  comparable,  it 
was  necessary  to  adjust  the  time  of  solution  A  to  that  of  solu- 
tion B,  since  in  this  way  both  hydrolysis  curves  can  be  plotted 
together.  The  time  for  solution  B,  when  its  rotation  was  the 
same  as  the  initial  rotation  of  A  (4.029°),  was  read  off  on  the 
curve  for  solution  B  and  found  to  be  61.50  minutes,  and  the 
values  given  in  the  parentheses  under  A  in  Table  II  are  the 
time  values  of  solution  A  adjusted  to  those  of  solution  B  by 
adding  61.50  minutes. 

The  Time  Element  is  Apparent  Only  in  the  Initial  Velocity. 

After  the  initial  stage  of  the  hydrolysis  has  been  passed,  the 
velocity  of  hydrolysis  gradually  decreases  and  becomes  the 
same  irrespective  of  whether  the  cane  sugar  solution  contained 
invert  sugar  or  not  at  the  beginning  of  the  reaction.  This  is 
shown  by  the  following  experiments. 

Two  solutions  were  prepared  exactly  like  solutions  A  and 
B  described  above.  This  time,  solution  A  was  allowed  to  react 
for  21  minutes  before  any  readings  were  made,  in  order  to  per- 
mit any  initial  effect  to  disappear  or  become  constant.  Sam- 
ples then  were  removed  and  examined  in  the  polariscope.  The 
changes  in  rotation  together  with  the  corresponding  times  cal- 
culated from  the  beginning  of  the  hydrolysis  are  given  under 
A  in  Table  III.  By  following  the  hydrolysis  of  solution  B  in 
the  same  way,  it  was  found  that  when  the  latter  had  been  un- 
dergoing hydrolysis  for  93.99  minutes  its  composition  was  the 
same  as  that  of  A  when  the  latter  had  been  undergoing  hydroly- 
sis for  30.9  minutes.  By  placing  this  point  of  solution  B  (93.99 
minutes  and  2.320°  rotation)  on  the  curve  for  solution  A,  in 
Figure  II,  at  the  point  where  A  has  the  same  rotation  (2.320°), 
we  find  that  this  corresponds1  in  time  to  30.9  minutes  for  solu- 
tion A.  By  subtracting  the  difference  between  these  two  times, 
93.99  —  30.9  or  63.09  minutes  from  the  time  values  of  solution 
B  (time  values  of  B  adjusted  to  those  of  A  are  given  in  the 
parenthesis  under  B  in  Table  III)  it  is  possible  to  plot  the  two 
curves  together  as  in  Figure  II. 

18 


TABLE   III. 

Temperature  25°.     Hydrogen  ion  cone.  10~4-4. 
Solution  A  (like  A  in  Table  II)  Solution  B  (like  B  in  Table  II) 


Time 
21.02 
24.01 
28.00 
32.02 
36.02 


Rotation 
2.8230 
2.670 
2.463 
2.265 
2.074 


Time 

93.99  (30.90) 
96.99  (33.90) 

101.00  (37.91) 

105.01  (41.92) 
109.03  (45.94) 


Rotation 
2.320° 
2.177 
1.994 
1.807 
1.632 


It  will  be  observed  that  over  that  portion  of  the  time  where 
the  two  hydrolysis  curves  overlap  that  they  appear  to  be  strict- 
ly superimposable  and  that,  by  inspection  at  least;  the  two 
curves  on  either  side  of  the  common  portion  still  form  a  con- 
tinuous curve.  This  indicates  that  the  two  solutions  are  now 
hydrolyzing  with  the  same  speed,  and  that  the  time  element,  or 
difference  in  velocity  only  occurs  when  one  solution  is  starting 
and  the  other  has  been  in  progress  for  some  time  as  indicated 
in  Figure  II. 

The  conclusion  drawn  from  the  data  given  in  Table  III  and 
Figure  II  is  supported  also  by  some  unpublished  results  from 
experiments  carried  out  in  this  laboratory  some  years  ago  by 
Dr.  F.  M.  Beegle.  Beegle  permitted  a  5%  cane  sugar  solu- 
tion (B)  to  hydrolyze  completely  with  invertase,  then  added  5 
grms.  more  of  finely  powdered  (so  that  solution  would  take 

/*r 


^ 

^ 

^ 

^ 

/ 

0  =  Part 
A  "  > 
GJ  » 

•  " 

A  -Ex  per  in 
A  - 
d- 

ent  L 
Z 
I 
JT 

^/ 

Y 

0                30               60               90               120             150              ISC 
Minutes 

Fro! 

19 

place  as  rapidly  as  possible)  cane  sugar  per  100  cc.  of  the  solu- 
tion and  allowed  the  hydrolysis  to  continue.  The  velocity  hy- 
drolysis of  the  added  portion  of  cane  sugar  was  then  compared 
with  the  velocity  of  a  10%  cane  sugar  solution  (A)  after  the 
latter  had  passed  the  50%  hydrolyzed  stage.  The  change  in 
rotation  of  the  solutions  and  the  corresponding  times  are  given 
in  Table  IV,  and  the  corresponding  graphs  in  Figure  III. 

The  calculated  rotation  of  the  10%  cane  sugar  solution  A 
when  50%  hydrolyzed  was  3.80°.  The  rotations  given  in 
Table  IV  were  determined  by  adding  5  cc.  of  a  sodium  car- 
bonate solution  to  20  cc.  of  the  sugar  solution  and  then  ex- 
amining it  in  the  polariscope  with  a  200  mm.  tube.  The  inver- 
tase  correction  for  the  rotations  in  this  set  of  experiments  was 
negligible.  By  subtracting  3.80°  from  the  initial  rotation  of 
solution  A,  10.64°,  6.84°  is  obtained  as  the  change  in  rotation 
corresponding  to  the  50%  hydrolysis  stage.  Locating  this 
point,  6.84°,  on  the  curve  in  Figure  III  and  reading  the  corre- 
sponding time  co-ordinate,  the  latter  was  found  to  be  82.0  min- 
utes. The  5%  hydrolyzed  cane  sugar  solutions  to  which  5% 
more  cane  sugar  had  been  added  (that  is  solutions  B  I  and 
B  IL in  Table  IV)  had,  in  the  case  of  B  I  a  rotation  3.44°  after 
the  reaction  had  been  in  progress  for  4.0  minutes.  Solution  A 
had  the  rotation  3.44°  after  it  had  been  undergoing  hydrolysis 
for  87.5  minutes  or  in  other  words  it  took  solution  A  87.5 — 
82.0  or  5.5  minutes  to  undergo  the  same  extent  of  hydrolysis 
as  solution  B  I  had  undergone  in  4.0  minutes.  Similarly  it  was 
found  that  solution  B  II  required  only  9.5  minutes  to  underg'o 
the  same  degree  of  hydrolysis  as  solution  A  underwent  in  11.3 
minutes.  This  again  shows,  as  was  demonstrated  by  the  data 
given  in  Table  II  that  the  initial  velocity,  in  the  case  of  solu- 
tion B,  is  greater  than  the  velocity  in  such  a  solution,  as  A, 
where  the  reaction  has  been  in  progress  for  some  time.  But  the 
data  in  Table  IV  also  shows,  as  can  be  seen  in  Figure  III,  that 
the  hydrolysis  curve  of  solution  B  is  super-imposable  upon  that 
of  solution  A  and  that  the  time-element  is  only  apparent  dur- 
ing the  initial  stage  of  a  hydrolysis  of  cane  sugar  by  invertase. 

Besides  the  experiments  of  Table  IV,  another  set  was  exam- 
ined in  which  2.5  grams  of  cane  sugar  per  100  cc.  solution  in- 

20 


stead  of  10  grams  were  used  and  the  velocity  of  hydrolysis  be- 
yond the  50%  stage  was  compared  with  that  of  a  solution  con- 
taining 1.25  grams  of  cane  sugar  and  1.25  grams  of  inverted 
sugar  per  100  cc.  solution.  These  curves  were  found  to  coin- 
cide also. 


TABLE  IV. 

Part  A.    10  grm's.  cane  sugar  per  100  cc.    Temp.  25°. 
Hydrogen  ion  cone.  —  10— i-2G     (200  mm.  tube). 


I. 


II. 


Time  in 

minutes 

Rotation 

0.0 

10.62° 

2.5 

10.44 

14.0 

9.35 

46.0 

6.60 

91.5 

3.27 

126.5 

1.26 

175.5 

—0.66 

00 

—3.06 

Time 

Rotation 

0.0 

10.64° 

17.0 

9.10 

59.0 

5.45 

101.5 

2.58 

144.5 

0.46 

176.0 

—0.70 

222.0 

—1.81 

260.0 

—2.20 

CO 

—3.04 

Part  B.    5  grms.  cane  sugar  and  5  grms.  inverted  cane  sugar  per  100  cc. 
Temp.,  Invertase  cone,  and  hydrogen  ion  cone,  same  as  in  A. 


II. 


Time                      Rotatioi 

0.0 

(  83.5) 

— 

4.0 

(  87.5) 

3.44° 

20.5 

(104.0) 

2.46 

55.0 

(138.5) 

0.75 

100.0 

(183.5) 

—0.89 

146.0 

(229.5) 

—1.90 

219.0 

(302.5) 

—2.60 

co 

— 

—3.09 

Time 


Rotation 


0.0 

(  83.5) 

— 

9.5 

(  93.0) 

3.08° 

42.5 

(126.0) 

1.25 

71.0 

(154.5) 

0.00 

102.5 

(186.0) 

—1.00 

132.5 

(216.0) 

-1.68 

164.0 

(247.5) 

—2.17 

225.5 

(309.0) 

—2.65 

Does  Invertase  Action  Involve  Two  or  More 
Consecutive  Reactions? 

It  will  be  observed  upon  inspection  of  the  curves,  in  Figure 
I,  part  C,  for  the  1%  cane  sugar  solutions  containing  3%  and 

21 


4%  added  glucose  that  they  are  slightly  convex  to  the  time 
axis  at  the  start,  or  in  other  words,  the  initial  velocity  of  hy- 
drolysis under  these  conditions  seems  to  increase.  This  in- 
creasing effect  is  so  small,  however,  and  the  measurements 
involve  the  determination  of  such  small  absolute  changes  in 
the  extent  of  the  hydrolysis  that  it  might  be  attributed  to  pos- 
sible experimental  errors.  It  was  decided  therefore  to  repeat 
these  determinations  in  somewhat  different  manner.  Instead 
of  using*  the  polariscope  which  is  accurate  in  this  case  to  1 
milligram  of  hydrolyzed  cane  sugar  in  50  cc.,  a  copper  reduc- 
tion method  (for  details  see  the  experimental  part  of  the  paper) 
which  has  a  higher  degree  of  precision,  0.1  milligram  of  hy- 
drolyzed cane  sugar  per  50  cc.  of  solution,  was  adopted. 

In  order  to  avoid  the  large  amount  of  cuprous  oxide  that 
would  be  formed  if  the  copper  method  were  used  in  the  case  of 
the  above  1%  cane  sugar  solution  containing  3%  or  4%  of 
added  glucose,  a  0.5%  cane  sugar  solution,  containing  no  add- 
ed glucose,  was  used.  This  solution  had  about  the  same  speed 
of  hydrolysis  as  the  1%  solution  under  the  above  conditions. 
A  hydrolysis  of  a  1%  cane  sugar  solution  without  any  added 
glucose  was  followed  also  by  means  of  the  copper  method  for 
the  sake  of  comparison,  Part  C,  Table  V.  In  Table  V  are 
given  the  results  obtained  and  these  results  are  plotted  also  in 
Figure  IV. 

Dr.  Vosburgh,  of  this  laboratory,  has  shown  (his  results  are 
to  be  published  shortly)  that  certain  invertase  preparations 
when  acidified  with  hydrochloric  acid  to  adjust  the  hydrogen 
ion  concentration  of  the  solution,  do  not  always  give  repro- 
ducible results.  For  this  reason,  the  hydrogen  ion  concentra- 
tion of  the  0.5%  cane  sugar  solution  was  adjusted  in  two  ways. 
The  results  given  in  Part  A  of  Table  V  were  obtained  by  using 
hydrochloric  acid,  and  those  in  Part  B  by  using  an  sodium  ace- 
tate-acetic acid  buffer  mixture.  In  this  way,  if  the  velocities 
obtained  in  the  two  cases  were  the  same  then  any  abnormality 
in  the  velocity  of  hydrolysis  that  might  appear  cannot  be  at- 
tributed to  the  method  of  adjusting  the  hydrogen  ion  concen- 
tration of  the  solutions. 

22 


TABLE    V. 

Part  A.    0.5%  cane  sugar  solution.    2  cc  Invertase  per  100  cc.  solution. 

Temperature  25°.    Hydrogen  ion,  1CM-4  moles  per  liter  and 

adjusted  by  means  of  HC1. 

Mg.  cane  sugar 

Time  Mg.  Cu.  hydrolyzed  per  50  cc. 

1.03  11.28  4.02 

2.14  22.95  9.30 

3.01  30.34  13.44 
4.03  40.37  18.14 
5.03  49.10  22.22 

6.03  .  57.52  26.20 
7.00                                65.46  30.09 
8.00                                74.15                               34.26 

9.04  82.25  38.23 

10.01  90.18  42.19 

11.02  98.16  46.20 

Part  B.    Same  solution  and  conditions  except  sodium  acetate — acetic 
acid  used  for  adjusting  the  hydrogen  ion  concentration; 

Mg.  cane  sugar 
Time  Mg.  Cu.  hydrolyzed  per  50  cc. 

1.03  12.62  4.30 

2.02  22.27  8.90 

3.04  31.56  13.43 

4.03  40.56  17.90 
5.03  48.95  22.02 
6.03  56.59  25.60 
7.00  64.25  29.35 

Part  C.    lc/c  cane  sugar  solution,  other  conditions  same  as  for  B. 

Mg.  cane  sugar 

Time  Mg.  Cu.  hydrolyzed  per  50  cc. 

0.52  13.78  3.22 

1.06  20.20  6.59 

1.56  27.17  9.82 

2.08  33.87  13.20 

2.65  41.19  16.75 

3.23  49.37  20.67 

3.88  58.86  25.72 

4.41  65.57  28.86 

From  the  data  in  Table  V  and  the  shape  of  the  curves  in  Figure 
IV,  it  is  evident  again  that  this  increase  in  the  initial  velocity 

23 


of  hydrolysis,  at  least  in  the  case  of  the  0.5%  cane  sugar  solu 
tion,  shows  up  just  as  in  the  case  of  the  curves  Part  C,  Figure  I 


48 


42. 


18 


0 

A 
0 


Part 


A 
6 
C 


6  9 

Minutes 

FIG.N 


12 


15 


To  gather  more  evidence  still  on  this  point,  the  results  ob- 
tained by  other  investigators  from  dilute  sugar  solutions  were 
examined  and  plotted  in  the  same  way.  Here  again  this  same 
increase  of  the  initial  velocity  was  found  to  occur.  Thus  ex- 
periments 31  A  and  31  B  of  Nelson  and  Vosburgh6  in  which  a 
0.4%  cane  sugar  solution  was  used  and  similar  experiments — 
7,  p.  337,  and  F,  p.  341- — described  by  Michaelis  and  Menten 
(loc.  cit.)  in  which  0.178%  and  0.821%  cane  sugar  solutions 


24 


respectively  were  used,  all  showed  this  increase  in  the  initial 
velocity. 

The  Retarding  Influence  of  Very  Small  Amounts  of  Glucose 
on  the  Velocity  of  Hydrolysis. 

TABLE  VI. 

Cone,  cane  sugar  =  1  g.  per  100  cc.      Cone.  Invertase=:0.5  cc.  per  100  cc. 
Cone.  Hydrogen  ion  =  10-4-4.    Temperature  =  25°. 


Cone,  of 

Rotation  after 

Change 

Glucose  % 

Init.  Rotation 

50  min. 

X100 

0.0 

358.830 

358.25° 

58 

0.5 

359.95 

359.43 

52 

1.0 

1.08 

0.60 

48 

2.0 

3.34 

2.92 

42 

3.0 

5.60 

5.23 

37 

4.0 

7.87 

7.52 

35 

\ 

\ 

^^ 

\ 

^^  63 

\ 

\ 

\ 

t 

\ 
\ 
\ 

1" 

\    x 

\\ 

£ 

\\ 

\\ 

Vb 

v\ 

1" 

\\ 

\\ 

^ 

\\ 

r 

\ 

i 

i" 

\ 

N 

^^ 

33 

123 
Cone.  Glucose  in  Grams 
per  100  cc. 
FIG.Y 

25 


In  Table  VI  is  recorded  the  data  obtained  in  studying  the 
retarding  influence  of  varying  amounts  of  added  glucose  upon 
the  rate  of  hydrolysis  of  a  1%  cane  sugar  solution.  It  will  be 
observed,  especially  by  the  inspection  of  curves  in  Figure  V, 
a  graph  of  the  data,  that,  although  the  retardation  is  increased 
by  augmenting  the  glucose  concentration,  yet  each  successive 
increment  of  the  retardant  has  less  and  less  effect.  Thus,  the 
measured  effect  of  0.5  grams  of  glucose  at  the  beginning  of  the 
reaction  is  58 — 52  or  6  units  (see  last  column  in  Table  VI) 
while  when  3  grams  were  added  then  a  decrease  of  21  units  was 
observed.  In  the  first  instance,  the  specific  retardation  (the 
specific  retardation  is  defined  as  the  influence  of  each  unit  of  1 
gram  of  glucose  under  the  conditions  of  the  experiment)  was 
58 — 52  or  12  and  in  the  last  58  —  34  or  7.  Furthermore 

0.5  ~T~ 

it  must  be  borne  in  mind  that  at  the  time,  50  minutes  after  the 
start  of  the  reaction*,  when  the  readings  were  made,  there  was 
present  in  the  solution  containing  no  glucose  about  0.17  grams 
per  100  cc.  of  invert  sugar  formed  in  the  hydrolysis  that  had 
taken  place  up  to  this  time.  If  the  retarding  influence  of  the 
invert  sugar  is  considered  as  practically  the  same  as  that  of 
glucose,  then  the~  specific  effect  of  the  0.17  grams  of  invert 
sugar  should  be  greater  than  that  of  0.5  grams  of  glucose,  since 
the  retarding  effect  increases  with  decreasing  amounts  of  the 
monoses  present.  If  this  is  true,  the  value  obtained  for  the 
"initial  velocity  of  hydrolysis"  must  be  too  low  due  to  the 
greater  specific  retardation  of  small  amounts.  This  merely 
points  out  that  the  measured  retardation  effects  of  the  small 
amounts  must  be  too  low  and  that  in  the  light  of  this  the 
true  curve  representing  the  retardation  should  rise  very  rapidly 
as  it  approaches  the  velocity  axis  and  may  possibly  be  asymp- 
totic to  it.  As  a  consequence,  the  probable  character  of  the 
true  retardation  curve  is  indicated  by  the  dotted  line  in  Fig- 
ure V. 


*  It  will  be  readily  seen  that,  if  there  be  no  time  effect  at  the  start 
of  ^  the  reaction,  the  change  in  rotation  after  50  minutes  will  be  on  the 
initial  linear  portion  of  the  hydrolysis  curve  with  this  concentration 
of  enzyme.  This  would  be  a  consequence  of  the  results  of  Nelson  and 
Vosburgh6,  who  have  shown  that  the  velocity  of  the  reaction  is  propor- 
tional to  the  invertase  concentration. 

26 


The  retarding  effect  of  the  invert  sugar,  as  it  is  formed,  there- 
fore should  cause  a  hydrolysis  curve  of  a  cane  sugar  solution 
to  fall  off  rapidly  from  the  start.  This  is,  however,  not  the 
case,  as  has  been  shown  above.  A  tentative  explanation  there- 
fore suggests  itself,  that  some  other  phenomenon  besides  re- 
tardation occurs  which  tends  to  offset  the  latter,  thus  giving 
rise  to  the  constant  or  slightly  increasing  initial  velocities  ob- 
tained in  this  work. 

EXPERIMENTAL 

Preparation  of  Invertase.  The  invertase  was  prepared  from 
yeast  which  had  been  allowed  to  autolyze.  The  filtered  solu- 
tion had  been  kept  in  a  stoppered  bottle  for  about  three  years 
previous  to  its  purification.  In  general,  the  procedure  followed 
was  that  described  by  Nelson  and  Born7.  It  was  found  that 
treatment  of  the  autolyzed  and  filtered  yeast  solution  with  am- 
monia (stirring  to  prevent  local  alkalinity)  until  it  was  just 
short  of  being  neutral  to  litmus,  was  very  helpful  in  removing 
the  precipitate  obtained  by  the  lead  acetate.  The  invertase 
was  not  precipitated  again  after  dialysis  but  was  treated  with 
toluene,  bottled  and  kept  in  an  ice-box.  No  loss  in  activity 
was  noticed  throughout  the  period  of  the  investigation. 

Cane  Sugar.  The  cane  sugar  used  was  a  good  commercial 
grade  such  as  Domino  or  Jack  Frost  which  had  been  recrystal- 
lized  from  alcohol  according  to  the  method  of  Cohen  and  Com- 
nielin8  and  dried  in  a  0.04  mm.  vacuum  at  50°  over  sulphuric 
acid. 

Glucose  and  Fructose.  The  glucose  was  a  very  pure  com- 
mercial grade,  obtained  from  the  Corn  Products  Co.,  N.  Y., 
and  was  recrystallized  from  acetic  acid  according  to  the  method 
of  Hudson  and  Dale9.  It  was  washed  with  alcohol  and  dried  at 
50°  over  sulphuric  acid  at  0.04  mm.  In  order  to  remove  the 
last  traces  of  acetic  acid,  the  drying  was  repeated  over  stick 
caustic  soda. 

The  fructose  was  twice  recrystallized  from  acetic  acid  ac- 
cording to  Vosburgh10.  It  was  noticed,  that,  if  the  alcohol 
washings  were  combined  with  the  filtrate  and  if  the  mixture 

27 


were  placed  in  the  ice-box,  a  large  quantity  of  fructose  could 
be  recovered  after  about  a  week's  standing.  The  fructose  was 
dried  in  the  same  manner  as  the,  glucose,  except  that  the  tem- 
perature was  maintained  at  30°.  To  prevent  decomposition 
and  absorption  of  moisture,  the  sugars  were  kept  in  the  dark 
in  stoppered  bottles  inside  a  dessicator.  They  all  exhibited  the 
correct  rotations. 

The  invert  sugar  used  in  this  work  was  made  up  from  equal 
quantities  of  glucose  and  fructose. 

Preparation  of  Solutions,  Table  I.  The  method,  with  a  few 
modifications,  described  by  Nelson  and  Vosburgh6  was  used 
for  the  experiments  given  in  Table  I.  200  cc.  of  a  sugar  solu- 
tion, of  twice  the  concentration,  required,  were  added  to  an 
equal  volume  of  invertase  solution,  also  of  twice  the  required 
concentration.  A  stream  of  air  was  blown  through  the  solu- 
tion to  insure  rapid  and  thorough  mixing.  Both  the  cane  sugar 
and  invertase  solutions  had  been  kept  in  the  thermostat  for  at 
least  2  hours  before  mixing  to  permit  them  to  acquire  the  cor- 
rect temperature. 

Solutions,  Table  II,  III  and  V.  The  cane  sugar  solutions  in 
this  case,  were  made  up  by  the  aid  of  specific  gravity  tables11 
and  corrected  for  25°  according  to  Schonrock's  formula11.  The 
required  amount  of  powdered  cane  sugar  was  placed  in  a  non- 
sol  bottle.  Water  and  the  required  amount  of  buffer  were 
added  so  that  on  the  addition  of  a  definite  volume  of  stock  in- 
vertase solution  (18.05  cc.  or  some  other  selected  quantity)  the 
final  volume  would  be  exactly  900  cc.  Vigorous  agitation  by 
a  current  of  air  was  resorted  to. 

Solutions,  Table  VII.  The  same  procedure  was  followed  as 
described  for  solutions,  Table  I,  save  that  25  cc.  portions  of 
sugar  and  invertase  solutions  were  used  instead  of  200  cc. 

Hydrogen  ion  adjustment.  All  the  experiments  were  car- 
ried out  at  a  hydrogen  ion  concentration  of  1CH-4  moles  per 
liter.  For  experiments  described  in  Tables  I  and  V,  Part  A, 
0.01  molar  hydrochloric  acid  was  used  according  to  the  method 
of  Nelson  and  Vosburgh6  (that  is — comparing  the  solutions 

28 


colorimetrically  with  citrate  solutions  that  had  been  standard- 
ized by  the  electrometric  method).  In  the  electrometric  stand- 
ardization of  the  citrate  solutions,  a  saturated  potassium  chlor- 
ide-calomel half  cell  and  a  saturated  potassium  chloride  bridge 
were  used  (Fales  and  Mudge12).  In  all  the  other  solutions  the 
hydrogen  ion  concentration  was  adjusted  by  means  of  sodium 
acetate-acetic  acid  buffer  according  to  Michaelis13.  This  latter 
method  was  checked  and  found  satisfactory. 

Measurements  of  Volume  and  Time.  The  measuring  flasks, 
burettes  and  pipettes  were  carefully  calibrated.  In  the  experi- 
ments described  in  Tables  II,  III,  and  V,  the  pipettes  used  had 
a  time  delivery  from  8  to  12  seconds  in  order  to  eliminate  any 
error  in  ascertaining  the  time  of  stopping  the  reaction  when 
taken  as  a  mean.  The  18  cc.  invertase  pipette  delivered  in  7.5 
seconds.  They  were  all  held  vertically  and  removed  when  the 
free  flow  ceased.  It  was  found  that  an  operator  can  duplicate 
results  by  this  method  with  a  precision  of  better  than  ±  0.01  cc. 
In  the  other  experiments  ordinary  calibrated  pipettes  were 
employed. 

The  time  of  delivery  of  the  pipettes  and  the  length  of  time 
of  the  reactions  (that  is — the  time  from  the  introduction  of 
the  enzyme  to  the  interruption  of  the  hydrolysis)  were  follow- 
ed with  a  stop  watch  which  could  be  read<  to  0.2  of  a  second 
and  therefore  the  time  intervals  in  all  the  Tables,  except  I,  are 
precise  to  at  least  0.01  minute. 

All  weights  are  so-called  "weights  in  air." 

Stopping  the  reaction.  The  reaction  was  stopped  by  run- 
ning the  50  cc.  samples  from  the  reaction  bottle  in  the  thermo- 
stat, into  5  cc.  of  0.2  molar  sodium  carbonate.  The  procedure 
was  reversed  in  the  experiments  of  Table  VII.  In  those  of 
Table  I  this  operation  was  done  in  60  cc.  flasks  and  then  made 
up  to  volume. 

Determination  of  Extent  of  Hydrolysis.  In  all  the  experi- 
ments save  those  recorded  in  Table  V,  the  degree  of  hydrolysis 
was  determined  in  a  400  mm.  jacketed  tube  which  had  been 
calibrated.  The  temperature  was  maintained  at  25.00°  ±  0.05° 

29 


by  pumping  water  through  the  tube  from  the  thermostat.   The 
hydrolyses  were  all  conducted  at  25.043°  ±  0.005°. 

A  Schmidt  and  Haensch  triple  field  instrument  at  a  half 
shadow  angle  of  2°  was  used  in  conjunction  with  a  1,500  candle 
power  quartz  mercury  .vapor  lamp.  The  light  was  filtered 
through  an  Eastman  No.  74  Wratten  filter  which  had  been  test- 
ed with  a  Lummer-Brodhun  spectrophotometer.  This  test 
showed  that  practically  none  of  the  mercury  lines  was  trans- 
mitted except  546  ^  ^  Readings  could  be  made  after  some 
practice  with  a  precision  better  than  0.01°. 

Determination  of  Initial  Angle.  In  obtaining  the  initial 
angles,  Table  I,  25  cc.  of  water  and  25  cc.  of  cane  sugar  solu- 
tion of  double  strength  were  run  into  5  cc.  of  sodium  carbonate 
solution,  and  this  made  up  to  60  cc.  and  read  in  the  polariscope. 
A  correction  was  then  made  for  the  rotation  that  the  invertase 
would  have  if  present.  In  the  other  experiments,  instead  of 
the  25  cc.  of  water,  25  cc.  of  a  double  strength  invertase  solu- 
tion were  employed  so  as  to  conform  to  the  rest  of  the  readings 
in  the  same  experiments. 

Copper  Method.  The  method  of  Thomas  and  Quisumbing 
of  this  laboratory,  which  is  to  be  published  soon,  was  used  for 
determining  the  degree  of  hydrolysis  in  Table  V. 

Beakers,  containing  50  cc.  samples,  5  cc.  0.2  M  sodium  car- 
bonate and  25  cc.  each  of  the  modified  Fehliug's  solutions  A 
and  B,  were  immersed  in  a  water  bath  kept  at  80°  —  1°.  for 
30  minutes.  The  cuprous  oxide  was  filtered  off,  washed  and 
dissolved  in  dilute  nitric  acid.  A  small  amount  of  sulphuric 
acid  was  added  to  this  solution  which  was  evaporated  to  dry- 
ness  on  a  hot  plate.  The  copper  was  determined  finally  by  the 
thiosulphate  method. 

To  construct  the  calibration  curves  for  "reducing  sugar",  the 
following  procedure  was  employed.  Standard  cane  sugar  and 
invert  sugar  solutions  were  made  up.  Definite  amounts  of 
these  were  added  to  5  cc.  of  sodium  carbonate  into  which  the 
correct  number  of  cc.  of  invertase  solution  had  been  run  prev- 
iously. Water  was  then  added  so  that  the  final  volume  would 
be  55  cc.  The  analysis  was  then  performed  as  described  above. 
The  addition  of  the  invertase  was  necessary  as  it  formed  a  cop- 

30 


per  compound  and  thus  tended  to  make  the  results  too  high 
unless  allowed  for.  As  the  amount  of  this  copper  compound 
varied  with  the  concentrations  of  the  other  substances  present, 
it  could  not  be  corrected  for  and  was  therefore  included  in  the 
calibration  mixture.  These  calibration  curves  were  construct- 
ed separately  for  each  hydrolysis  in  order  to  eliminate  any 
error  due  to  varying  composition  of  the  Fehling's  solutions. 
The  data  for  these  curves  are  given  in  Table  VIII. 

TABLE    VIII. 


For  PartA, 

Table  V 

For  Part  B, 

Table  V 

For  Part  C, 

Table  V 

Mg.  Cane 

Mg.  Cane 

Mg.  Cane 

Sugar  hydrol 

.     Mg.  of 

Sugar  hydrol 

.     Mg.  of 

Sugar  hydrol 

.     Mg.  of 

per  50  cc. 

Copper 

per  50  cc. 

Copper 

per  50  cc. 

Copper 

0.00 

2.61 

0.00 

2.73 

0.00 

6.02 

2.00 

5.29 

2.00 

6.51 

2.00 

11.09 

4.00 

11.80 

4.00 

11.93 

4.00 

15.47 

6.00 

16.45 

6.00 

16.34 

6.00 

19.08 

8.00 

20.73 

8.00 

20.49 

8.40 

23.77 

10.00 

23.98 

10.00 

24.63 

9.60 

26.75 

20.00 

44.33 

15.00 

35.68 

15.00 

37.46 

30.00 

65.25 

20.00 

44.87 

20.00 

48.11 

40.00 

85.85 

25.00 

55.40 

25.00 

57.40 

50.00 

105.62 

30.00 

65.67 

30.00 

68.01 

35.00 

75.05 

The  points  on  the  curves  were  so  chosen  that  they  corre- 
sponded to  every  two  milligrams  of  cane  sugar  hydrolyzed  up 
to  the  first  10  milligrams  and  to  every  five  or  ten  milligrams 
of  hydrolyzed  cane  sugar  thereafter. 

SUMMARY 

(1)  The  initial  velocity  of  the  hydrolysis  of  cane  sugar  in 
the  presence  of  invertase  was  found  generally  to  be  constant 
for  a  considerable  period  after  the  beginning  of  the  reaction. 

(2)  A  sucrose  solution,  containing  added  invert  sugar,  hy- 
drolyses  with  a  different  initial  velocity  than  that  manifested 
during  the  reaction  by  a  partially  hydrolyzed  cane  sugar  solu- 
tion of  the  same  composition. 

(3)  This  difference  in  influence  upon  the  velocity  of  the  hy- 
drolysis, between  invert  sugar  added  to  the  reaction  at  its  be- 

31 


ginning1  and  that  formed  during  the  hydrolysis,  renders  the 
method  of  Michaelis  and  Menten  for  determining  the  dissocia- 
tion constants  of  the  so-called  sugar-invertase  compounds 
valueless. 

(4)  It  was  found  that  the  initial  velocity  of  hydrolysis  of 
dilute  sucrose  solutions  or  solutions  to  which  a  considerable 
amount  of  glucose  had  been  added  appeared  to  increase  for  a 
short  period  after  the  beginning  of  the  reaction. 

(5)  The  specific  retardation  due  to  glucose  decreases  as 
the  concentration  of  hexose  is  increased  and  finally  reaches  a 
minimum.    This  indicates  that  the  true  initial  velocity  may  be 
very  great  and  (when  the  facts  in  section  4  are  considered) 
that  the  hydrolysis  probably  consists  of  a  series  of  consecutive 
reactions. 


32 


BIBLIOGRAPHY 

1  Henri — Lois  generates  de  1'action  des  diastases.  Paris  (1903). 
•-  Brown—/.  Chem.  Soc.,  81,  373,  (1902). 

3  Hudson—/.  Am.  Chcm.  Soc.,  30,  1160,  1564,  (1908). 

4  Armstrong— Proc.  Roy.  Soc.,  73,  516,  (1904). 

5  Michaelis  and  Menten — Biochem.  Zeit.,  49,  333,  (1913). 

"  Nelson  and  Vosburgh— /.  Am.  Chem.  Soc.,  39,  797,  (1917). 

7  Nelson  and  Born—/.  Am.  Chem.  Soc.,  36,  393,  (1914). 

8  Cohen  and  Commelin — Z.  physik.  Chcm.,  64,  29,  (1908). 

9  Hudson  and  Dale—/.  Am.  Chem.  Soc.,  39,  790,  (1917). 

10  Vosburg-h— /.  Am.  Chem.  Soc.,  42,  1696,  (1920). 

11  Browne — Handbook  of  Sugar  Analysis,  (1st  edition),  page 

30  and  appendix,  page  1. 

12  Kales  and  Mudge— /.  Am.  Chem.  Soc.,  42,  2434,  (1920). 

12  Michaelis — Die  Wasserstoffionenkonsentration,  page  184. 

13  Colin  and  Chaudun— Compt.  Rend.,  167,  338,  (1918). 


VITA 

Harold  Lester  Simons  was  born  in  New  York  City  on  July 
15,  1897.  He  graduated  from  the  College  of  the  City  of  New 
York  in  June,  1917,  receiving  the  degree  of  Bachelor  of  Arts. 
He  entered  the  Graduate  School  of  Pure  Science  of  Columbia 
University  in  July,  1917,  and  received  therefrom  the  degree  of 
Master  of  Arts  in  June,  1918.  He  was  Laboratory  Assistant  in 
Chemistry  at  that  institution  from  February,  1918  to  February, 
1919.  He  was  co-author  (with  Dr.  H.  L.  Fisher)  of  a  paper 
on  "Dimethyl  Tartronate"  published  in  the  Journal  of  the 
American  Chemical  Society,  43,  628,  (1921). 


THXS 


DATE 


AN  INITIAL  PINE  OF  25  CENTS 


APR 


9    1938 
'46  DL 


LD  21-95w-7,'37 


Gay  lord  Bros. 

Makers 

Syracuse,  N.  Y 
PAT.,  "  "M 


YC  39876 


151782 


55" 


UNIVERSITY  OF  CALIFORNIA  LIBRARY 


1 

/ 


